Rules of referral
The descriptive gain achieved by exponence rules is confined to the relation between features and individual forms. Exponence rules define the structure of word forms directly, and characterize the structure of a morphological system indirectly, as derivative of the properties of single forms. Although they are sometimes described as ‘extended WP models’, realizational approaches do not adopt the complex system perspective of a classical WP model (see Chapter 7), but instead exhibit a simple organization. The feature constraints of a language define a set of distinctive feature bundles, and a set of realization rules determines the formal spell-out of those bundles. The collection of individually well-formed bundle-form pairs constitutes the morphological system. A realizational model makes no assumptions about the interdependency of forms of the kind that underlie the classical factorization of morphological systems into exemplary paradigms and principal parts. Hence a morphological system in which the realization of each cell of a paradigm is fully independent of the realization of every other cell is no less amenable to a realizational analysis than a system in which the choices are systematically interdependent.
In classical WP models, proportional analogies can be used to express impli- cational dependencies as well as exponence relations because proportions relate feature-form pairs, not single feature bundles and forms. For example, the proportions in (5.4) above, repeated in (6.2), exhibit patterns of ‘Priscianic’ syncretism that cannot be treated as simple feature spell-out.
(6.2) Priscianic analogy in Latin conjugations
a. florere : florerem = esse : essem
b. amatus : amaturus = monitus : moniturus
Many, though by no means all, realizational models include rule types that express these kinds of ‘Priscianic’ or ‘parasitic’ dependencies. This family of rule types includes the ‘parasitic derivations’ of Matthews (1972:185), the ‘morphological transformations’ of Matthews (1991), the ‘takeovers’ of Carstairs (1987), and the ‘referral’ rules of Zwicky (1985) and Stump (1993b, 2001). The rule that Matthews (1991:194) proposes for (6.2a), repeated in Figure 6.9, illustrates some common properties of this rule type.
This rule plainly does not spell out a feature bundle, but instead relates the spell-outs of two distinct bundles, a present infinitive bundle, which is realized by ‘X, and a 1sg imperfect subjunctive bundle, which is realized by ‘X+m’. As the distinct features in these bundles show, the correspondence defined by the rule is purely at the level of form. There need be no intrinsic relation between the features in these bundles, since the features serve solely to locate a particular pair of cells in a conjugational paradigm. In the present case, there is no sense in which the features of the present infinitive underlie or contribute to those of the imperfect subjunctive. Yet since the rule in Figure 6.9 relates two exponence rules, it preserves the interpretive character of exponence rules.
On what might seem like the simplest and most obvious interpretation of this rule, it expresses a direct dependency between two paradigm cells, so that the
Figure 6.9 Latin present infinitive-imperfect subjunctive correspondence definition of the isg imperfect subjunctive form of a verb involves retrieving the present active infinitive form ‘X’ of that verb and then adding the inflection -m. However, this is not a possible interpretation of Figure 6.9 in an orthodox realizational model. Each form is defined independently, and in the course of deriving one form of a verb, other surface forms of that same verb are not available. A realizational model contains stem entries, realization rules, feature inventories and constraints, and, depending on the model, a predefined ‘space’ of wellformed bundles, possibly organized into abstract paradigms. But these models contain no repository of surface forms that a rule could reference. The surface forms of a language exist only as potential outputs; they are not stored in instantiated paradigms or otherwise ‘cached’ by a realizational model. The fact that non-basic units have no permanent status again reflects the realizational focus on exponence relations at the level of single forms.
The treatment of whole-word syncretism is similarly constrained in expanded realizational models, which again contain no persistent units larger than the stem. The model of Paradigm Function Morphology (PFM; Stump 2001) provides a clear illustration. An innovative feature of PFM is the role assigned to ‘paradigm functions’ of the form PF[a ] (p), where a represents the features of a paradigm cell and p is the root of a lexeme. The value of a paradigm function PF[a ] (p) is the form that realizes cell a of a lexeme p. Hence it might appear that whole-word referrals could be expressed in terms of paradigm functions. As Stump (1993b) suggests, a constraint PF[aj](p) = PF^] (p) would relate the realization of cells ai and aj of a lexeme p:
one might assume that a rule of referral encompasses whole words. On this assumption, the rule of referral determining the form of Macedonian impf padnese ‘you (sg.) fell’ would simply fill the 2sg imperfect cell in the paradigm of padn- with the form padnese ‘s/he fell’ occupying the 3sg imperfect cell in that paradigm. Viewed in this way, the relevant rule of referral could be stated as a restriction on the evaluation of a paradigm function ... (Stump
However, the introduction of paradigm functions does not change the fact that PFM, like other realizational models, realizes individual forms, not paradigms or larger collections of forms. In the course of evaluating a paradigm function PF[ai ](p), the value of other paradigm functions, including PF[aj](p), is undefined. The only way of obtaining a value from PF[aj](p) is to explicitly evaluate that function in the course of realizing the original paradigm function PF[ai](p). Consequently, there is no obvious way of incorporating a whole-word conception of referrals without construing them as essentially transderivational devices that invoke a sub-realization to obtain a form.
The ‘parasitic derivations’ of Matthews (1972) provide the earliest formulation of a referral relation in a realizational model. Parasitic derivations occupy a relatively minor role, defining a special case in a more general exponence relation. As expressed in the passage below, a derivation is ‘parasitic’ in the case when a rule r realizes a property p with reference to a property x:
where r refers in its reference-component either to p itself or to some morphosyntactic property x which is substituted forp in accordance with a previous rule. (Matthews 1972:185)
The idea of realizing a property p by proxy, i.e., by realizing a “property x which is substituted for p” is preserved in the subsequent ‘morphological transformations’ of Matthews (1991). Matthews suggests that these ‘transformations’ be interpreted as ‘metarules’, modelled on the metarules of GPSG accounts (Gazdar et al. 1985). On this interpretation, the rule in Figure 6.9 expresses a dependency, not between forms, but between exponence rules that define those forms. This dependency has two components. The first is that the present infinitive provides the base for the 1sg imperfect subjunctive and, more generally, for the entire imperfect subjunctive paradigm. The second is that 1sg imperfect subjunctive features are spelled out by -m. These components are expressed separately by the referral and exponence rules in Figure 6.10.
The exponence rule is a conventional spell-out rule, which applies in the inflectional rule block ‘C’. The referral, which applies in the stem-formation rule blocks ‘A’ and ‘B, has an essentially counterfactual force, allowing an imperfect subjunctive cell to be realized as if it contained present infinitive features. This rule must be interpreted counterfactually and cannot be construed as defining a new feature bundle in which present infinitive features are substituted for imperfect subjunctive features. This substitution would yield an ill-formed bundle, since 1sg and imperative features do not co-occur in Latin.
The referral in Figure 6.10 expresses the dependency between imperfect subjunctive and present infinitive cells. What is required next are the rules that realize the infinitive form. These are provided in Figure 6.11.
Figure 6.10 Latin stem referral and 1sg exponence rule
Figure 6.11 Present theme vowel and infinitive rule
Figure 6.12 Root form and isg imperfect subjunctive cell of floreo flower’
Figure 6.13 Priscianic realization of isg imperfect subjunctive
The definition of surface word forms from stems in a realizational model inverts the abstractive perspective of a classical WP grammar, in which “the Present stem [is] obtained by dropping -re of the Pres. Inf. Active” (Gildersleeve and Lodge 1895:71). As discussed in Chapter 5.2, this analytical inversion creates difficulties in assigning determinate features to stems and stem formatives. To sidestep these issues, which are orthogonal to the status of referral rules, the first rule in Figure 6.11 just associates the second declension theme vowel -e with the feature ‘present’ (and also suppresses declension class ‘features’). The second rule likewise spells out infinitive features by -re. The rules in Figures 6.10 and 6.11 can then realize the 1sg imperfective subjunctive cell in Figure 6.12, which contains the root form of
The realization offlorerem is exhibited in Figure 6.13. The process is seeded by the feature bundle and root form from the cell in Figure 6.12. There are no rules that directly realize this bundle in blocks A and B, so the bundle is initially realized by the rules that interpret the boxed features, which are introduced by the referral rule in Figure 6.10. The referred features are realized in block A by the present theme vowel rule, which introduces -e, and in block B by the infinitival rule, which adds -re. Block C contains the 1sg exponence rule in Figure 6.10, which interprets the original bundle by adding -m.
The realization offlorerem illustrates how the form dependency between distinct paradigm cells can be expressed by referral rules. Because this dependency is expressed not by borrowing the infinitive form but by applying the rules that define that form, there is no representation of the fact that the Priscianic base florere is itself a surface form. Hence full-word syncretism plays no special role in a realizational model, apart from the fact that surface forms realize a determinate bundle of features associated with a paradigm cell.
Sub-word stem syncretism is therefore amenable to a similar analysis. To express the Priscianic pattern in (6.2b), a realizational model can decompose the
Figure 6.14 Latin past passive-future active stem correspondence
Figure 6.15 Latin first conjugation past passive participle stem rule
Figure 6.16 Latin future active participle stem rule
Figure 6.17 Root form and future active participle cell of Latin amo ‘love’
correspondence between ‘X’ and ‘X + tir’ into the sub-generalizations expressed by the rules in Figures 6.14-6.16. The rule in Figure 6.14 defines the future active participle stem as dependent on the past passive participle stem. The rule in Figure 6.15 introduces the stem formative for first conjugation verbs. The rule in Figure 6.16 then adds the future active stem formative.
Like previous rules, these rules apply in a fixed order, determined by their assignment to blocks. To ensure that at is realized before ur, the rule that identifies stems in Figure 6.14 triggers the application of the stem formation rule in Figure 6.15 before the application of the rule in Figure 6.16. This interaction is illustrated in Figure 6.18. The entry in Figure 6.17 specifies the features of the nominative singular future active participle cell and the root form am. The cell features in Figure 6.18 are initially interpreted by realizing the boxed past passive participle features, in accordance with the referral in Figure 6.14. The past participle stem rule in Figure 6.15 applies in block A, adding the first conjugation stem formative -at. The future active participle rule in Figure 6.16 applies to the original features in block B, adding -Ur. The resulting stem, amatur, defines the base for the future active participle paradigm.
Figure 6.18 Priscianic realization of future active participle stem
-  In this respect they contrast with rules in the IP model in Chapter 2.3, in which one form-featurepair is the input to a process that defines a new feature-form pair.
-  Though given that inflectional systems are, for all intents and purposes, finite, transderivationalreferrals do not raise the formal and computational issues discussed by Johnson and Lappin (1999) inconnection with transderivational syntactic devices.
-  In fact, isg is realized by -m more generally in active subjunctive and in active perfective paradigmsbut this refinement does not materially affect the analysis.